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Spearman's rho for zero-inflated count data: formulation and attainable bounds

Jasper Arends, Guanjie Lyu, Mhamed Mesfioui, Elisa Perrone, Julien Trufin

Abstract

We propose an alternative formulation of Spearman's rho for zero-inflated count data. The formulation yields an estimator with explicitly attainable bounds, facilitating interpretation in settings where the standard range [-1,1] is no longer informative.

Spearman's rho for zero-inflated count data: formulation and attainable bounds

Abstract

We propose an alternative formulation of Spearman's rho for zero-inflated count data. The formulation yields an estimator with explicitly attainable bounds, facilitating interpretation in settings where the standard range [-1,1] is no longer informative.

Paper Structure

This paper contains 14 sections, 2 theorems, 54 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background and notation
  3. Estimator and attainable bounds
  4. Estimator of Spearman's rho for zero-inflated count data
  5. Attainable bounds for Spearman's rho
  6. Simulation study and empirical application
  7. Simulation study
  8. Case study
  9. Conclusion
  10. Proof of Theorem 1
  11. Proof of Proposition 1
  12. Upper bound
  13. Lower bound
  14. Simulation results

Key Result

Theorem 1

For bivariate zero-inflated count data, Spearman's rho is given by

Figures (2)

  • Figure 1: Simulation results for $\alpha = 0.5$ and $N = 150$ samples, based on 1000 repetitions.
  • Figure S.1: QQ-plots of $\hat{\rho}_A$ with sample size $N = 1000$ under various parameter configurations. The simulations are based on 1000 repetitions.

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • Proposition 1